This is a problem from Ch. 18 in the essential college physics book. 87.) A part

Question

This is a problem from Ch. 18 in the essential college physics book.

87.) A particle carrying a -1.4µC charge moves at 185 m/s through a uniform 45 mT magnetic field pointing in the +y direction. The resulting force on the particle is 9.3µN in the +z direction. In what direction is the particle moving?

The answer is already posted on Chegg but I am trying to understand why it is that this equation (F=qvBsin) is rearanged for v and solved for when in the question it states that it is moving at 185 m/s already.

Explanation / Answer

formula fo rmagnetic force acting on particle is

F = qvBsin theta

sin theta = F/ qvB

theta = sin^-1 ( F/ qvB)

= sin^-1 ( 9.3* 10^-6 N/ 1.4* 10^-6 ( 185) ( 45* 10^-3)

=52.93 degree

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